toe-in:
if toe-in is increased, temperature should go up by more friction ?

Ackermann:
does have Ackermann any influence to tyre temperature?

I think track temperature is not that essential, because the heat tranfer area is too small.
But what´s with the air around the tyre?
Can they cool the tyre by directing air to the tyre or through the wheel over the rim (from inside; but there is the hot break?...)

I think track temperature is not that essential, because the heat tranfer area is too small.

Track temperature will noticeably transfer with the tire temperature. It's just that you can't do much to change the effect. If you change tire pressure, for example, that's going to affect a lot more things and more significantly than it will change the transfer area.

I have never met a racecar that uses toe in. Toe out always, more nervous, drags on straights but steering reaction is always better. Toe in is for the tow car!!

It depends upon the car and driver. What are the characteristics of the car, i.e. Ackerman, bump steer etc ? Driver preference for feel of the car is also key.There have been real race cars through the years that used front toe-in when raced in period.